Euclidean $n$-planes in pseudo-euclidean spaces and differential geometry of Cartan domains

Euclidean «-planes in Pseudo-euclidean Spaces and Differential Geometry of Cartan Domains

Spatial Analysis in curved spaces with Non-Euclidean Geometry

The ultimate goal of spatial information, both as part of technology and as science, is to answer questions and issues related to space, place, and location. Therefore, geometry is widely used for description, storage, and analysis. Undoubtedly, one of the most essential features of spatial information is geometric features, and one of the most obvious types of analysis is the geometric type an...

Lines on Planes in n-Dimensional Euclidean Spaces

The notation and terminology used here are introduced in the following papers: [1], [5], [12], [4], [9], [14], [13], [8], [15], [6], [2], [3], [7], [11], and [10]. We follow the rules: a, a1, a2, a3, b, b1, b2, b3, r, s, t, u are real numbers, n is a natural number, and x0, x, x1, x2, x3, y0, y, y1, y2, y3 are elements of R . One can prove the following propositions: (1) s t · (u · x) = s·u t ·...

Phone classification in pseudo-euclidean vector spaces

Recently we have proposed a structural framework for modelling speech, which is based on patterns of phonological distinctive features, a linguistically well-motivated alternative to standard vector-space acoustic models like HMMs. This framework gives considerable representational freedom by working with features that have explicit linguistic interpretation, but at the expense of the ability t...

Spaces of pseudo - Riemannian geodesics and pseudo - Euclidean billiards Boris

In pseudo-Riemannian geometry the spaces of space-like and timelike geodesics on a pseudo-Riemannian manifold have natural symplectic structures (just like in the Riemannian case), while the space of light-like geodesics has a natural contact structure. Furthermore, the space of all geodesics has a structure of a Jacobi manifold. We describe the geometry of these structures and their generaliza...